Make up: Project presentation class at the end of the semester Announcement No Class on Thursday, October 25th Make up: Project presentation class at the end of the semester

Lecture Objectives: Review Linearization of nonlinear equation for unsteady state problems

Linearization of radiation equations Surface to surface radiation Equations for internal surfaces - closed envelope Ti Tj Linearized equations: Calculate h based on temperatures from previous time step

Linearized radiation means linear system of equations Calculated based on temperature values from previous time step B0 C0 T0 F0 A1 B1 C1 T1 F1 A2 B2 C2 T2 F2 These coefficient will have Some radiation convection coefficients x = A3 B3 C3 T3 F3 A4 B4 C4 T4 F4 A5 B5 C5 T5 F5 A6 B6 T6 F6

Energy balance for air unsteady-state heat transfer QHVAC

System of equation for more than one element Roof air Left wall Right wall Floor Elements are connected by: Convection – air node Radiation – surface nodes

Example Tair is unknown and it is solved by system of equation :

System of equations (matrix) for single zone (room) 8 elements Three diagonal matrix for each element x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x Air equation

Impacts on HW3 …..

System of equations for a building Matrix for the whole building 4 rooms Rom matrixes Connected by common wall elements and airflow in-between room – Airflow simulation program (for example CONTAM) Energy Simulation program “meet” Airflow simulation program

Next assignment: Project 1 We will use software: http://www.doe2.com/equest/ Soon we will have a class in the computer lab

Modeling steps Define the domain Analyze the most important phenomena and define the most important elements Discretize the elements and define the connection Write energy and mass balance equations Solve the equations Present the result ES program Preprocessor Solver Postprocessor

Characteristic parameters Conduction (and accumulation) solution method finite dif (explicit, implicit), response functions Time steps Meteorological data Radiation and convection models (extern. & intern.) Windows and shading Infiltration models Conduction to the ground HVAC and control models

Weather File Typical Meteorological Year TMY, TMY2, TMY3 http://rredc.nrel.gov/solar/old_data/nsrdb/1991-2005/tmy3/

eQUEST (DOE2) US Department of Energy & California utility customers eQUEST - interface for the DOE-2 solver DOE-2 - one of the most widely used ES program - recognized as the industry standard eQUEST very user friendly interface Good for life-cycle cost and parametric analyses Not very large capabilities for modeling of different HVAC systems Many simplified models Certain limitations related to research application - no capabilities for detailed modeling